Distribution of Angular Momentum in the Transverse Plane

TL;DR

This paper clarifies that the Fourier transform of the second moment of GPDs does not represent the angular momentum distribution in the transverse plane for a longitudinally polarized nucleon, challenging a common interpretation.

Contribution

It demonstrates that the Fourier transform of the second moment of GPDs does not correspond to the angular momentum distribution in the transverse plane for a longitudinally polarized target.

Findings

Fourier transform of GPDs' second moment does not depict angular momentum distribution.

Challenges the widely accepted interpretation of GPD moments in spin decomposition.

Provides theoretical clarification on the limitations of GPD Fourier transforms.

Abstract

Fourier transforms of GPDs describe the distribution of partons in the transverse plane. The 2nd moment of GPDs has been identified by X.Ji with the angular momentum (orbital plus spin) carried by the quarks - a fundamental result that is being widely utilized in the spin decomposition of a longitudinally polarized nucleon. However, I will demonstrate that, despite the above results, the Fourier transform of the 2nd moment of GPDs does not describe the distribution of angular momentum in the transverse plane for a longitudinally polarized target.